Heap Data Structure is generally taught with Heapsort. Heapsort algorithm has limited uses because Quicksort is better in practice. Nevertheless, the Heap data structure itself is enormously used. Following are some uses other than Heapsort. The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as “heaps”, regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority.
Priority Queues: Priority queues can be efficiently implemented using Binary Heap because it supports insert(), delete() and extractmax(), decreaseKey() operations in O(logn) time. Binomoial Heap and Fibonacci Heap are variations of Binary Heap. These variations perform union also in O(logn) time which is a O(n) operation in Binary Heap. Heap Implemented priority queues are used in Graph algorithms like Prim’s Algorithm and Dijkstra’s algorithm.
Order statistics: The Heap data structure can be used to efficiently find the kth smallest (or largest) element in an array.
Creation
- create-heap: create an empty heap
- heapify: create a heap out of given array of elements
- merge (union): joining two heaps to form a valid new heap containing all the elements of both, preserving the original heaps.
- meld: joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps.
Inspection
- size: return the number of items in the heap.
- is-empty: return true if the heap is empty, false otherwise.
Internal
- increase-key or decrease-key: updating a key within a max- or min-heap, respectively
- delete: delete an arbitrary node (followed by moving last node and sifting to maintain heap)